======================
Generate reduced model
======================

This step illustrates how to generate a `Reduced System Model` (RSM) from the random sampling scan in the previous section.
The RSM is a parameterization of the global tokamak variable 
such as the normalized plasma pressure ``betaN``, bootstrap current fraction ``fBS``, toroidal field hoop stress  ``stress_hoop`` etc 
as a function of the Tokamak design and operation parameters. 
TokDeisigner supports a range of Machine Learning techniques including Log-linear (LL) regression, Gaussian Process (GP), and Neural Network (NN). 
TokDesigner workflows often start with the LL regression, providing a clear dependency of the global tokamak variables 
to the  design and operation parameters (like ITER energy confinement scaling of Elmy H-mode plasmas ``tua98``). 
In addition, the constraints can be described by a linear system of equations.

Template 
--------

`example3 <https://github.com/ORNL-Fusion/tokdesigner-doc/tree/main/examples/example1>`_

Reduced Model
-------------

**Command line**

.. code-block:: bash

    preprocess.py --data=db.dat --train=db_train.dat -- test=db_test.dat --ratio=0.2

The preprocess.py splits the data ``db.dat`` into the train data (``db_train.dat``) and the test data (``db_test.dat``). This example uses 20 % (``--ratio=0.2``) of the input data for test.

.. code-block:: bash
 
   fitdb.py --input=fitdb.json --train=db_train.dat --test=db_test.dat --output=fitout.json

The fitdb.py generates a reduced model using the train dataset (``db_train.dat``) and evaluates the reduced model accuracy using the test dataset (``db_test.dat``). As an example, the normalized pressure  ``betaN`` are parameterized as a function of the scan variables ``aratio``, ``fgw_ped``, ``nepeak``, ``pinj``, and ``h98``. The bootstrap current fraction ``fbs`` and  the fusion power ``pfus`` are parameterized as a function of ``aratio``, ``fgw_ped``, ``nepeak`` and ``betaN``

.. note::

  The choice of the independent variables are crucial to the accuracy of the reduced models. Obviousely, the scan variables are good initial try, but not necessarily best represents the system. This topic will appear in many places in the following sections.

**fitdb.json**

.. code-block:: python

  {
  "fbs": {
      "model":"linear",
      "scaler_x":"log",
      "scaler_y":"log",
      "variables": [
          "aratio", "fgw_ped", "nepeak", "betan"], 
      "parameter": {
      }
  },

  "pfus": {
      "model":"linear",
      "scaler_x":"log",
      "scaler_y":"log",
      "variables": [
          "aratio", "fgw_ped", "nepeak", "betan"], 
      "parameter": {
      }
  },

  "betan": {
      "model":"linear",
      "scaler_x":"log",
      "scaler_y":"log",
      "variables": [
          "aratio", "pinj", "fgw_ped", "nepeak", "h98"], 
      "parameter": {
      }
  }
  }

See also the `Neural Network <https://github.com/ORNL-Fusion/tokdesigner-doc/tree/main/docs/under_construction.rst>`_
reduced model example.

**fitout.json**

The output file ``fitout.json`` contains the coefficients of the LL regression.

.. code-block:: python

  {
      "fbs": [
          "loglinear",
          {
              "const": 0.18823371506585898,
              "aratio": -0.4430942101868331,
              "fgw_ped": -0.1350619408712145,
              "nepeak": 0.21081006299692615,
              "betan": 1.1310480676370078
          }
      ],
      "pfus": [
          "loglinear",
          {
              "const": 1.64943792579016,
              "aratio": 1.207555937736708,
              "fgw_ped": -0.7255082562105468,
              "nepeak": -0.6954783516280638,
              "betan": 2.939140937783406
          }
      ],
      "betan": [
          "loglinear",
          {
              "const": 0.17639747416067017,
              "aratio": 0.8869343206322062,
              "pinj": 0.37591018633973355,
              "fgw_ped": 0.353477277768723,
              "nepeak": 0.3011398492024075,
              "h98": 1.8843684195879282
          }
      ]
  } 

.. image:: reduced_model.png
  :width: 800
  :align: center
  :alt: Reduced System Model